Suppose the yield on short-term government securities (perceived to be risk-free

Question

Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 9.0%. According to the capital asset pricing model: What is the expected return on the market portfolio? What would be the expected return on a zero-beta stock? Suppose you consider buying a share of stock at a price of $90. The stock is expected to pay a dividend of $12 next year and to sell then for $93. The stock risk has been evaluated at beta = - 5. Using the SML, calculate the fair rate of return for a stock with a beta = -0.5. Calculate the expected rate of return, using the expected price and dividend for next year.

Explanation / Answer

a) What is the expected rate of return on the market portfolio?

E[R=1] = Rf + (E[Rm] Rf )

= 4 % + 1( 9% 4%) = 9%

b) What would be the expected return on a stock with = 0?

                  E[R=0] = Rf + (E[Rm] Rf )

= 4% + 0 ( 9% 4%) = 4%

c)Suppose you consider buying a share of stock at $90. The stock is expected to pay $12 in dividends next year and you expect to sell it then for $93. The stock risk has been evaluated at = 0.5.

c-1 E[R=0.5] = Rf + (E[Rm] Rf )

= 4% 0.5( 9% 4%) = 1.5%

c-2 P0 = E[P1] + E[D1] / 1 + R

= 93 + 12/ 1 + 0.015 = $105.16

So the stock is underpriced according to the CAPM.

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